In the scene where Annemarie tells Von Sturm of her recent exploits as she prepares to bathe, the slip she is wearing is so sheer that it becomes see-through. This was not unusual for the pre-code era during which the production was filmed, but would have been considered too risque for a movie of the post-code era which immediately followed.
The story is based on a real German-trained spy in WWI who used the code name "Fraulein Doktor". She ran a training school for spies in Antwerp, Belgium during the city's German occupation. According to a biography of Myrna Loy, the studio had to be careful about how the character was portrayed as she was still alive and there was a risk of a libel suit.
The soundtrack and scenery was all wrong for Istanbul, shockingly wrong, as if Istanbul was medieval Baghdad as opposed to 20th century Anatolia. More importantly, and similarly, the two times that they showed messages (1 theatrical announcement, and 1 message to Ali Bey) in Ottoman Turkish, the messages were actually written in Arabic, not Turkish.